Relation of voltage to current So far we have pictured simply the voltage on the line, but that voltage is of course
accompanied by a current. We now ask what relation this current has to the voltage.
To find the relation between voltage and current, we substitute v back in equation 2.6
and integrate with respect to time, and obtain where f(z) is the constant of integration.
We substitute this result back into equation 2.6 and obtain the result f0(z) = 0,
i.e. f(z) = constant. This constant term corresponds to a steady d.c. voltage, which
we set to zero, as we are not interested in a superimposed d.c. solution. Hence, the above relation becomes. A little investigation will show that the parameter Z0 has the dimensions of resistance
and its units are thus ohms.
It is however common to call Z0 the characteristic impedance rather than the characteristic
resistance. This is done because because we will encounter, in a later section
dealing with the analysis of sinusoidal waves on a transmission line, a concept which is
properly called characteristic impedance and which has a defining equation which is formally
identical with equation 2.12. It is traditional to recognise that homology by the use
of the same terminology, even though doing so disguises the reality that in the present
context Z0 is really a resistance, and that in the present context the concept of impedance
has no meaning.
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